| IV. |
Learning Objectives |
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A. Solve first order differential equations by
the methods such as separable equations, exact equations, homogeneous equations,
linear equations, and direction fields. |
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B. Understand the existence and uniqueness of
solutions, the structure of solutions of linear equations, and the concept
of linear independence and its relationship to the Wronskian. |
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C. Solve linear equations with constant coefficients
by the methods of variation of parameters and undetermined coefficients. |
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D. Solve linear systems of differential equations
by the methods of elimination and eigenvalues. |
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E. Use Laplace transforms in the solutions of
equations. |
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F. Use power series in the solution of equations. |
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G. Applications of ordinary differential equations. |
| V. |
Academic Integrity |
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The very nature of higher education requires that students
adhere to accepted standards of academic integrity. Therefore Oakton Community
College has adopted a Code of Academic Conduct and a Statement of Student
Academic Integrity. These may be found in the Student Handbook. You may
also find a summary of the Code of Academic Conduct on the College Catalog.
Among the violations of academic integrity listed and defined are: Cheating,
plagiarism, falsification and fabrication of records and official documents,
personal misrepresentation and proxy, and bribes, favors, and threats. |
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It is the student's responsibility to be aware of behaviors
that constitute academic dishonesty. |
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Pursuant to the due process guarantees contained in the
Policy and Procedures on Student Academic Integrity, the minimum punishment
for the first offense for a student found in violation of the standards
of academic integrity is failure in the assignment. In addition, a disciplinary
record will be established and kept on file in the office of the Vice-President
for Student Affairs for a period of 3 years. |
| VI. |
Outline of Topics |
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A. First Order
Differential Equations |
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1. Linear equations |
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2. Separable equations |
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3. Exact equations |
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4. Integrating factors |
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5. Systems of linear equations |
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6. Use of technology to solve differential equations and systems |
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B. Second Order
Linear Differential Equations |
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1. Homogeneous equations |
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2. Reduction methods for order of equations |
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3. Homogeneous equations with constant coefficients |
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4. Complex roots of auxiliary equations |
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5. Nonhomogeneous equations |
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6. Method of undetermined coefficients |
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7. Method of variation of parameters |
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8 Use of technology to support calculations |
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C. Applications |
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1. Growth and decay |
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2. Mechanics |
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3. Vibrations |
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4. Spring-mass systems |
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5. Electric circuits |
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D. Numeric methods |
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1. Direction fields |
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2. Euler's method |
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3. Modified Euler's method |
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4. Runge-Kutta method |
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5. Use of technology to demonstrate methods |
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E. LaPlace transform |
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1. Properties of the LaPlace transform |
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2. Inverse transform and solution of initial value problems |
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3. Use of the LaPlace transform for discontinuous functions |
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4. Convolutions calculated by the LaPlace transform |
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5. Use of technology to calculate LaPlace transforms |
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F. Power series |
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1. Power and Taylor series |
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2. Regular and ordinary singular points |
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3. Frobenius' method |